A multivariate bias correction method for a two-stage climate model considering inconsistencies

Abstract

The present invention discloses a two-stage climate model multivariate bias correction method considering inconsistency, firstly, climate variables are selected to obtain climate model data and observation data; the model data and observation data are spatially interpolated to a uniform resolution; the quantile increment mapping method is used to perform single variable bias correction on each climate variable; and the correlation between multiple variables is corrected using a free distribution shuffle algorithm considering inconsistency. This method divides the multivariate bias correction into two stages, single variable correction and correlation correction, based on the consideration of inconsistency. The calculation is fast and simple, applicable to all climate variables, and can be expanded to multiple dimensions, which is conducive to improving the accuracy of climate model prediction of meteorological and hydrological elements.

Description

Technical Field

[0001] The invention belongs to the technical field of climate model bias correction, and relates to a two-stage climate model multivariate bias correction method considering inconsistency. Background Art

[0002] The Global Climate Model (GCM) is an important tool for climate simulation and the only tool for predicting future climate scenarios. In recent years, it has been widely used in climate change impact assessment research. However, due to model system errors and computational constraints, there is a large deviation between the data output by GCM and the actual climate state. Bias correction is a basic technique for correcting the output results of climate models based on measured data. Its main principle is to establish a statistical relationship between the observed meteorological and climate variables and the corresponding climate model simulation results, and then apply this relationship to future periods to obtain the corrected climate model prediction results for future periods.

[0003] Most existing bias correction techniques are based on independent correction of a single climate variable, without considering the bias of correlation between multiple variables. When using multiple meteorological variables output by a climate model to drive a meteorological or hydrological model, this single variable bias correction technique inherits the correlation bias of the original climate model output, resulting in great uncertainty in the output results of the meteorological or hydrological model. Therefore, inventing a bias correction method that can correct the correlation between variables while correcting each climate variable is of great significance for scientifically and accurately assessing the impact of climate change.

[0004] For example, patent CN117078037A discloses a method for bias correction of daily climate variables in spatial grids of future climate scenarios, and the specific method is: spatial interpolation of daily climate variable data observed on the ground to generate a specified climate variable observation data matrix for the historical period; correction of the time dimension of the specified climate variable observation data matrix for the historical period, the specified climate variable simulation data matrix for the future period, and the specified climate variable simulation data matrix for the historical period; determination of the daily average absolute change matrix and the daily average relative change matrix based on the corrected specified climate variable simulation data matrix for the future period and the corrected specified climate variable simulation data matrix for the historical period; bias correction of the corrected specified climate variable observation data matrix for the historical period using the daily average absolute change matrix and the daily average relative change matrix to generate future climate forecast data. This method first corrects the time dimension, and then uses the daily average absolute change matrix and the daily average relative change matrix to bias correct the corrected specified climate variable observation data matrix for the historical period. It is a typical method for independently correcting a single climate variable, inheriting the correlation bias between climate variables output by the original climate model, resulting in great uncertainty in the output results of the meteorological or hydrological model.

[0005] Traditional bias correction methods are generally based on the consistency assumption, that is, climate variables in the future and historical periods have the same statistical characteristics. However, in the context of climate change, this assumption is often inconsistent with the actual situation, that is, the historical and future climate characteristics are inconsistent. Therefore, adding a module that considers inconsistency to the traditional multivariate bias correction method based on the consistency assumption has great theoretical and practical value in this field.

[0006] Prior art CN112765912A discloses that a multivariate bias correction method is used to correct the output data of a global climate model to obtain corrected global climate model data, thereby obtaining a global climate model meteorological sequence under a climate change scenario. During the correction process, the quantile mapping method is first used to correct the deviations of the global climate model output variables at each quantile, wherein the output variables are daily precipitation, daily maximum temperature, and daily minimum temperature; then the correlation relationship between the corrected temperature and precipitation variables is reconstructed to obtain a corrected global climate model meteorological sequence. However, the correction process does not take into account the inconsistency of historical and future climate characteristics, so the corrected meteorological data still has a large gap with the actual. Summary of the invention

[0007] In view of the shortcomings of the existing technology, the present invention proposes a two-stage climate model multivariate bias correction method considering inconsistency. This method introduces the inconsistency idea into the multivariate bias correction method for the first time, and divides the multivariate bias correction into two stages: the first stage independently corrects each single variable, and the second stage corrects the correlation between variables. It can be applied to the post-processing of global climate model data, reduce the uncertainty of climate variable simulation prediction, and improve the credibility of climate change impact assessment.

[0008] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0009] In one aspect, the present invention provides a two-stage climate model multivariate bias correction method considering inconsistency, comprising the following steps:

[0010] Select a number of climate variables according to actual needs, and obtain the simulated data series output by the global climate model and the observed data series of the selected climate variables;

[0011] Interpolate the simulated data series and the observed data series onto a spatial grid of the same resolution;

[0012] Each climate variable was corrected separately using the univariate bias correction method;

[0013] The correlation between climate variables was corrected using a multivariate correlation correction method that takes into account inconsistency.

[0014] Preferably, the statistical time resolution of the simulated data sequence and the observed data sequence is the same, which is any one of daily data, weekly data and monthly data.

[0015] Preferably, climate variables include but are not limited to temperature, humidity, wind speed, precipitation, solar radiation, etc.

[0016] Preferably, in order to maintain data consistency, the data on February 29 in leap years needs to be removed.

[0017] Preferably, the simulation data sequence output by the global climate model includes model simulation data for historical periods and model prediction data for future periods.

[0018] Preferably, the observation data sequence includes a grid observation data sequence and a site observation data sequence, and the simulation data sequence and the grid observation data sequence are interpolated onto the spatial grid using bilinear interpolation, and the site observation data sequence is interpolated onto the spatial grid using Kriging interpolation.

[0019] Preferably, the spatial grid is represented by a latitude and longitude grid, and the grid side length is 0.5°-10°.

[0020] Preferably, the univariate bias correction method adopts the quantile increment mapping method, and the transfer function adopts the non-parametric empirical distribution function:

[0021]

[0022]

[0023]

[0024] In the formula, x bc,h (t), x bc,f (t) are the corrected historical and future period model data, respectively, x m,h (t), x m,f (t) are the historical and future period model data before correction, respectively, and F o,h is the cumulative distribution function of the observed data in the historical period, F m,h is the cumulative distribution function of the historical period model simulation data, F m,f is the cumulative distribution function of the model forecast data for the future period, Δ m (t) is the gain factor of the model in the future period relative to the historical period.

[0025] Preferably, the multivariate correlation correction method considering inconsistency is a free distribution shuffle algorithm considering inconsistency, which specifically includes the following steps:

[0026] For each grid point of the spatial grid, a two-dimensional multivariate matrix X of historical period pattern simulation data, future period pattern prediction data, and historical period observation data series is constructed. h , X f , X o ; The length of the behavioral sequence in the two-dimensional multivariate matrix is ​​the variable, and the variable data is the data corrected by the univariate bias correction method;

[0027] Calculate the two-dimensional multivariate matrix X separately h , X f , X o The normal score matrix W h , W f , W o ;

[0028] For the normal score matrix W h , W f , W o Perform Kolleski decomposition to obtain three upper triangular matrices U h , U f , U o ;

[0029] Calculate the two-dimensional multivariate matrix X separately h , X f The new normal score matrix

[0030] The two-dimensional multivariate matrix X h , X f According to the new normal score matrix The rank relationship is readjusted to obtain the two-dimensional multivariate matrix completed in the second stage of correction

[0031] On the other hand, the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned two-stage climate model multivariable bias correction method when executing the program.

[0032] On the other hand, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned two-stage climate model multivariate bias correction method.

[0033] On the other hand, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements the above-mentioned two-stage climate model multivariate bias correction method.

[0034] In addition, the climate model data before and after correction can be compared and analyzed to analyze the correction effect of the multivariate correlation correction method considering inconsistency. Specifically, the Pearson correlation coefficients of daily precipitation and daily maximum temperature in the validation period (① original GCM output, ② univariate correction, ③ multivariate bias correction under the traditional consistency assumption, and ④ multivariate bias correction of the two-stage climate model considering inconsistency) are compared with the Pearson correlation coefficient corresponding to the observation data in the validation period. The smaller the deviation, the closer the correlation after correction is to the correlation of the observation data, and the better the correction effect.

[0035] It can be seen from the above technical solution that compared with the existing bias correction method, the two-stage climate model multivariate bias correction method considering inconsistency proposed in the present invention has the following advantages:

[0036] 1. In addition to correcting the bias of each climate variable, this method also introduces a scrambling algorithm to correct the correlation between variables;

[0037] 2. This method takes into account inconsistency when correcting the bias of multivariate correlations in climate model data. Compared with the traditional correction method under the consistency assumption, it can reduce the uncertainty of GCM prediction data and improve the accuracy of climate change impact estimates;

[0038] 3. This method divides multivariate bias correction into two stages: univariate correction and correlation correction. There is no need to fit the joint distribution of multivariate, which greatly simplifies the calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flow chart of a two-stage climate model multivariate bias correction method considering inconsistency disclosed in the present invention;

[0040] Figure 2 This is a comparison chart of the verification period in an implementation case of the present invention, wherein: Figure 2 Scatter density plots of the Pearson correlation coefficients of daily precipitation and daily maximum temperature after correction of (a) original climate model output, (b) univariate bias correction, (c) bivariate correction under traditional consistency assumption, and (d) the two-stage climate model multivariate bias correction method considering inconsistency proposed in this invention and the Pearson correlation coefficients of daily precipitation and daily maximum temperature of observed data. DETAILED DESCRIPTION

[0041] The following embodiments of the present invention are described in further detail in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0042] It should be noted that there are no mandatory restrictions on the time periods, regions, and variable expressions involved in the embodiments of the present invention, and they can be used for data correction of any climate variable, any GCM, any future climate scenario, and any time period; the embodiment of the present invention selects the CPC measured precipitation product as the measured data only as an example. For other research areas or other climate variables, measured data should be selected according to actual conditions.

[0043] Reference Figure 1 As shown, the calculation steps of the embodiment of the present invention are:

[0044] Step 1: With precipitation and daily maximum temperature as climate variables, download the daily precipitation and daily maximum temperature data from 1979 to 2014 output by the ACCESS-CM2 global climate model of the Sixth International Coupled Model Intercomparison Project (CMIP6) under the r1i1p1f1 operation experiment (referred to as GCM data or model data), and download the daily precipitation and daily maximum temperature data from 1979 to 2014 of the CPC product of the Climate Prediction Center of the National Atmospheric and Oceanic Administration of the United States as observation data (referred to as CPC data or observation data). In order to improve the accuracy of the correction, the data on February 29 of all years of all data are excluded, and 1979-1999 is used as the rate period (i.e., the "historical period" mentioned above), with a total of 7665 days of data, and 2000-2014 is used as the validation period (i.e., the "future period" mentioned above), with a total of 5475 days of data.

[0045] Step 2: Use bilinear interpolation to interpolate GCM data and CPC data to a spatial grid with a resolution of 1°×1°. Specifically, during the rate period, the daily precipitation and daily maximum temperature data simulated by the climate model can form matrices [X_his_pr] and [X_his_tmax] of 180×360×7665, respectively, where the rows are the sequence length and the columns are the variables; the observed daily precipitation and daily maximum temperature data can form matrices [X_obs_pr] and [X_obs_tmax] of 180×360×7665, respectively; during the validation period, the daily precipitation and daily maximum temperature data predicted by the climate model can form matrices [X_fut_pr] and [X_fut_tmax] of 180×360×5475, respectively.

[0046] Step 3: Use quantile increment mapping to correct the univariate bias. For each grid in space, use the quantile increment mapping method to correct the daily precipitation and daily maximum temperature data output by the global climate model. Specifically, taking daily precipitation as an example, for grid i, the 1×7665, 1×7665, and 1×5475 sequences of [X_his_pr], [X_obs_pr], and [X_fut_pr] in grid i are the rate-periodic model simulation data sequences x m,h , rate regular observation data series x o,hAnd the validation period model predicts the data series x m ,f, respectively calculate x m,h 、x o,h and x m,f The cumulative empirical distribution function F m,h 、F o,h 、F m ,f, and use formulas (1)-(3) to calculate the corrected rate-periodic model simulation data sequence x bc,h And the validation period model predicts the data series x bc ,f:

[0047]

[0048]

[0049]

[0050] In the above formula, t is a time series. In this embodiment, t is a day series. For example, x m,h (t) represents the climate variable (daily precipitation or daily maximum temperature) on the tth day of the ith grid in the data sequence simulated by the periodic model.

[0051] Substitute the daily precipitation observation data x of the regular series into the above formula respectively. o,h _pr, daily maximum temperature observation data x o,h _tmax, daily precipitation pattern data x m,h _pr, daily maximum temperature model data x m,h _tmax; daily precipitation pattern data x during the validation period m,f _pr, daily maximum temperature model data x m,f _tmax. Calculate the daily precipitation pattern data x at regular intervals after univariate bias correction bc,h _pr, daily maximum temperature model data x bc,h _tmax and daily precipitation pattern data x during the validation period after univariate correction bcf _pr, daily maximum temperature model data x bcf _tmax.

[0052] Step 4: The correlation between daily precipitation and daily maximum temperature is corrected by using the multivariate correlation correction method considering inconsistency. A two-dimensional multivariate matrix X of the rate-periodic model simulation data, rate-periodic observation data, and validation period model prediction data series is constructed for each grid point of the spatial grid. h , X o , X f Specifically, the method is as follows:

[0053] Step 4.1: In this embodiment, the climate variables are daily precipitation and daily maximum temperature. Therefore, a bivariate matrix Z is first constructed, with the first column being daily precipitation and the second column being daily maximum temperature: The daily precipitation pattern data x after the rate period univariate bias correction is bc,h _pr and daily maximum temperature model data x bc,h _tmax constitutes the variable matrix Z of the periodic pattern data h ; The rate of regular daily precipitation observation data x o,h _pr and daily maximum temperature observation data x o,h _tmax constitutes the observation data variable matrix Z o ; The daily precipitation pattern data x after univariate bias correction in the validation period (“future period”) bc,f _pr and daily maximum temperature model data x bc,f _tmax constitutes the validation period mode data variable matrix Z f The rows of the three variable matrices are all sequence lengths (7665 rows in total for the rate period and 5475 rows in total for the validation period), and the columns are variables.

[0054] Step 4.2: Calculate the variable matrix Z of the rate-periodic pattern data using formula (4): h , rate regular observation data variable matrix Z o , Validation period variable matrix Z f The normal score matrix W h , W o , W f :

[0055]

[0056] In the formula, i is the data in the variable matrix (Z h , Z o , Z f ) in each column, n is the variable matrix (Z h , Z o , Z f )The total number of samples in each column, is the inverse function of the normal distribution.

[0057] Step 4.3: Perform Kholesky decomposition on the normal score matrices of the rate-periodic pattern data, rate-periodic observation data, and validation period pattern data to obtain the corresponding upper triangular matrix U h , U o , U f , the formula is:

[0058] W=[U T ×U] Formula (5)

[0059] U is the upper triangular matrix in the score matrix.

[0060] Step 4.4: Calculate the rate period and validation period pattern data (two-dimensional multivariate matrix X) using formula (6) and formula (7) respectively. h , X f )’s new normal score matrix:

[0061]

[0062]

[0063] Where W h and Normal score matrix of the regular pattern data before and after correction, W f and The normal score matrix of the validation period model data before and after correction, U h , U o , U f are the upper triangular matrices of rate-periodic pattern data, rate-periodic observation data, and validation period pattern data, respectively.

[0064] Step 4.5: Convert the rate-regular pattern data bivariate matrix Z h , validation period model data bivariate matrix Z f Press The rank relationship is rearranged to obtain the corrected completion rate regular pattern bivariate matrix Validation period mode bivariate matrix The first column of the new bivariate matrix is ​​the corrected daily precipitation, and the second column is the corrected daily maximum temperature.

[0065] Verify the correction effect of the method of the present invention. Specifically, the validation period observation data selected in this embodiment is used as the standard data, and compared with the validation period model data corrected by the method of the present invention, and the scatter density diagrams of the Pearson correlation coefficients of the daily precipitation and daily maximum temperature of the validation period original GCM output, univariate correction, multivariate bias correction under the traditional consistency assumption, and multivariate bias correction of the two-stage climate model considering inconsistency and the Pearson correlation coefficients of the corresponding observation data of the validation period are drawn, respectively, see Figure 2 .

[0066] Figure 2 Each sub-graph in the figure shows the consistency between the correlation between global daily precipitation and daily maximum temperature during the validation period under each correction scheme (vertical axis) and the observed data (horizontal axis). The more concentrated the blue scattered points in the figure are and the closer they are to the 45° black diagonal solid line, the better the correction effect. Figure 2 As can be seen from the four sub-figures in , the univariate correction ( Figure 2 (b) The original output of the climate model ( Figure 2The correlation in (a) has almost no correction ability, and the traditional bivariate correction method under the consistency assumption ( Figure 2 (c)) has a certain correction ability for the correlation between variables, but the two-stage climate model multivariate bias correction method considering inconsistency proposed in this paper ( Figure 2 (d) has a stronger correction capability, which is reflected in Figure 2 The points in (d) are more concentrated, and the dark blue points are closer to the 45° black diagonal line.

[0067] In addition, it should be pointed out that, limited by the currently available observation data, this embodiment uses 1979-1999 as the rate period ("historical period") and 2000-2014 as the verification period ("future period"), which is only 20 years apart, and the climate change effect is not very significant. In the actual application of climate model data, it is often necessary to calibrate the climate model prediction data for the future period of 2020-2100. At this time, the impact of climate change under a time span of up to 100 years is very large, and inconsistency must be considered. Therefore, in the prediction and evaluation of climate change response in the future period, the two-stage climate model multivariate bias correction method considering inconsistency proposed by the present invention will show greater advantages than the correction method under the traditional consistency assumption.

[0068] The above embodiments are only used to illustrate the present invention, but not to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that various combinations, modifications or equivalent substitutions of the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and should be included in the scope of the claims of the present invention.

Claims

1. A two-stage climate model multivariate bias correction method considering inconsistency, characterized in that: The following steps are involved: Select a number of climate variables according to actual needs, and obtain the simulated data series output by the global climate model and the observed data series of the selected climate variables; Interpolate the simulated data series and the observed data series onto a spatial grid of the same resolution; The simulated data were corrected for each climate variable separately using the univariate bias correction method; The correlation between climate variables in the simulated data was corrected by using the multivariate correlation correction method considering inconsistency. The univariate bias correction method uses the quantile increment mapping method, and the transfer function uses the non-parametric empirical distribution function: In the formula, , They are the corrected historical and future period model data respectively. For the historical and future period model data before correction, is the cumulative distribution function of the observed data in the historical period, is the cumulative distribution function of the simulated data for the historical period pattern, is the cumulative distribution function of the model forecast data for future periods, is the gain factor of the model's future period relative to the historical period; The multivariate correlation correction method considering inconsistency is a free distribution shuffle algorithm considering inconsistency, which specifically includes the following steps: For each grid point of the spatial grid, a two-dimensional multivariate matrix of historical period pattern simulation data, future period pattern prediction data, and historical period observation data series is constructed. X h , X f , X o ; The length of the behavioral sequence in the two-dimensional multivariate matrix is ​​the variable, and the variable data is the data corrected by the univariate bias correction method; Calculate the two-dimensional multivariate matrix separately X h , X f , X o The normal score matrix of W h , W f , W o ; For the normal score matrix W h , W f , W o Perform the Kolleski decomposition and obtain three upper triangular matrices U h , U f , U o ; Calculate the two-dimensional multivariate matrix separately X h , X f The new normal score matrix , ,in, , ; The two-dimensional multivariate matrix X h , X f According to the new normal score matrix , The rank relationship is readjusted to obtain the two-dimensional multivariate matrix completed in the second stage of correction , .

2. The two-stage climate model multivariate bias correction method considering inconsistency according to claim 1, characterized in that: The statistical time resolution of the simulated data sequence and the observed data sequence is the same, which is any one of daily data, weekly data and monthly data.

3. The two-stage climate model multivariate bias correction method considering inconsistency according to claim 1, characterized in that: The simulation data sequence output by the global climate model includes model simulation data for historical periods and model prediction data for future periods.

4. The two-stage climate model multivariate bias correction method considering inconsistency according to claim 1, characterized in that: The observation data sequence includes a grid observation data sequence and a station observation data sequence. The simulation data sequence and the grid observation data sequence are interpolated onto the spatial grid using bilinear interpolation, and the station observation data sequence is interpolated onto the spatial grid using Kriging interpolation.

5. The two-stage climate model multivariate bias correction method considering inconsistency according to claim 1, characterized in that: The spatial grid is represented by a latitude and longitude grid, and the grid side length is 0.5°-10°.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the two-stage climate model multivariate bias correction method as described in any one of claims 1 to 5 is implemented.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the two-stage climate model multivariate bias correction method as described in any one of claims 1 to 5 is implemented.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the two-stage climate model multivariate bias correction method as described in any one of claims 1 to 5 is implemented.

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